The security elements of the Parkerian Hexad are:
Confidentiality Possession or Control Integrity Authenticity Availability Utility
Where do access controls (mandatory, discretionary and ACL) fit in?
Looking back at the wikipedia page you linked to, I can see access control falling into the first bullet, confidentiality.
Confidentiality refers to limits on who can get what kind of information. For example, executives concerned about protecting their enterprise’s strategic plans from competitors; individuals are concerned about unauthorized access to their financial records.
Access controls are exactly about who can get what kind of information.
In the comments below the answer, someone suggested it would be within authenticity and I was leaning towards that too but after reading what Wikipedia says, authenticity is more about proving that what you claim is true. Access control is about determining what it is you can do with that claim. Access control assumes that the claims are authentic.
If you go to the CIA triad definition of confidentiality, you will find the same approach as in the Parkerian hexad:
In information security, confidentiality "is the property, that information is not made available or disclosed to unauthorized individuals, entities, or processes" (Excerpt ISO27000).
So access controls (be it ACL, RBAC, or ABAC) belong to confidentiality.
Controls of any type are implementation mechanisms; the Parkerian Hexad are goals or assets. You would implement access controls to ensure that the set of potential actions affecting these goals are limited to only the set of actions that are explicitly permitted.
Access controls are an answer to the question: